Maybe it's because he was engaged to their niece and they decided to pick him instead of another employee at the company.
shareWere the Dukes having a three-some with their niece or something?
I am thinking that selecting Winthorpe was a little bit more than random - more personal than just business.
Why was Winthorpe selected by the Dukes?
Bored millionaires that they are, Randolph and Mortimer Duke make a bet (for $1) that they can completely change two men's lots in life just by giving one of them every opportunity while stripping away every opportunity the other formerly possessed. Mortimer doesn't think it can be done. Randolph, however, proves that if you take away patrician Winthorpe's job, home, friends, and reputation, he will become a vile reprobate despite the 'class' and breeding conferred upon him before that point. Meanwhile, if they gave vile reprobate, Valentine, Winthorpe's job, home, colleagues, and respect he could become every bit patrician that Winthorpe formerly was.
They choose Winthorpe because ostensibly they've known him all his life. His father was a colleague of theirs. Winthorpe, Jr. (Dan Ackroyd) was born and raised to eventually work at Duke Bros. So they knew he had all the breeding, reputation, and trappings of wealth to serve as an ideal test case.
Trading Places was a modern retelling of the classic story, The Prince and the Pauper.